Download April 26 -- Energy Practice

Kinetic Energy and Potential Energy
Name ________________________________
1. What is the gravitational potential energy of a 61.2 kg person standing on the roof of a 10-story building relative to (a) the tenth
floor, (b) the sixth floor, (c) the first floor? (Each story is 2.50 m high.)
2. A 1.00 x 104 kg airplane lands, descending a vertical distance of 10.0 km while travelling 100. km measured along the ground.
What is the plane's loss of potential energy?
3. Calculate the kinetic energy of a 45 gram golf ball travelling at: (a) 20. m/s, (b) 40. m/s, (c) 60. m/s.
4. How fast must a 1000. kg car be moving to have a kinetic energy of:
(a) 2.0 x 103 J,
(b) 2.0 x 105 J,
(c) 1.0 kWh?
5. A coconut falls out of a tree 12.0 m above the ground and hits a bystander 3.00 m tall on the top of the head. It bounces back up
1.50 m before falling to the ground. If the mass of the coconut is 2.00 kg, calculate the potential energy of the coconut relative to the
ground at each of the following sites:
(a) while it is still in the tree,
(b) when it hits the bystander on the head,
(c) when it bounces up to its maximum height,
(d) when it lands on the ground,
(e) when it rolls into a groundhog hole, and falls 2.50 m to the bottom of the hole.
6. A 50.0 kg bicyclist on a 10.0 kg bicycle speeds up from 5.00 m/s to 10.0 m/s.
(a) What was the total kinetic energy before accelerating?
(b) What was the total kinetic energy after accelerating?
(c) How much work was done to increase the kinetic energy of the bicyclist?
(d) Is it more work to speed up from 0 to 5.00 m/s than from 5.00 to 10.0 m/s?
7. How high would you have to lift a 1000. kg car to give it a potential energy of:
(a) 2.0 x 103 J,
(b) 2.00 x 105 J,
(c) 1.00 kWh?
8. Calculate the potential energy of a 5.00 kg object sitting on a 3.00 meter high ledge.
9. A 10.0 kg rock is at the top of a 20.0 m. tall hill. How much potential energy does it have?
10. A 25 N object is 3.0 meters up. How much potential energy does it have?
11. How high up is a 3.00 kg object that has 300. J of energy?
12. A 4.00 kg rock is rolling 10.0 m/s. Find its kinetic energy.
13. An 8.0 kg cat is running 4.0 m/s. How much kinetic energy does it have?
14. A rolling ball has 18 J of kinetic energy and is rolling 3.0 m/s. Find its mass.
15. A 4.0 kg bird has 8.0 J of kinetic energy. How fast is it flying?
16. At the moment when a shotputter releases a 5.00 kg shot, the shot is 3.00 m above the ground and travelling at 15.0 m/s. It
reaches a maximum height of 14.5 m above the ground and then falls to the ground. If air resistance is negligible,
(a) What was the potential energy of the shot as it left the hand relative to the ground?
(b) What was the kinetic energy of the shot as it left the hand?
(c) What was the total energy of the shot as it left the hand?
(d) What was the total energy of the shot as it reached its maximum height?
(e) What was the potential energy of the shot at its maximum height?
(f) What was the kinetic energy of the shot at its maximum height?
(g) What was the kinetic energy of the shot just as it struck the ground?
17. A rubber band is stretched from its resting position a distance of 0.10 m. If the spring constant is 2.5 N/m, what is the force
exerted on the rubber band?
18. A 12 V car battery is found to be capable of storing 2.00 kWh of electrical energy. For a certain electric car, it is necessary to
develop 1.00 x 104 W of power to drive at 5.56 m/s.
(a) Suppose that the car has 10 such batteries which results in 10 times the energy. How long (in hours) could it run if all 10 of
them released all of their energy?
(b) How far (in kilometers) can the car go on its 10 batteries if they are fully charged?
19. If a spring is stretched a distance of 0.25 m with a force of 20. N, what is the value of the spring constant?
20. If the spring constant of a pogo stick is 3500. N/m and the weight of the person on the pogo stick is 700. N, how much is the
spring in the bottom of the pogo stick compressed?
21. A 20.0 kg cart on wheels has been pushed up against a wall with a spring (k = 244 N/m) between the wall and the cart. The spring
is compressed a distance of 0.100 m.
(a) What is the force of the spring on the cart?
(b) If an applied force of 20.0 N is applied toward the wall, what will the acceleration of the cart be?
22. A box having a mass of 1.50 kg is accelerated across a table at 1.50 m/s2. The coefficient of friction on the box is 0.300.
(a) What is the force being applied to the box? (Use: Fapp -fs = ma)
(b) If this force were applied by a spring, what would the spring constant have to be in order for the spring to be stretched to only
0.0800 m while pulling the box?
23. A spring (k = 2.3 N/m) is attached to an object of mass = 10. kg. If the object is hung from the ceiling by this spring, how much
would the spring be stretched?
24. If s =0.50, how much force must be applied to a spring (spring constant of 0.80 N/m) which is attached to a block of wood (mass
= 4.0 kg) in order to just begin to move the block? (Use: Fapp - fs = ma; Recall that f = µFN)
25. A 3.0 kg metal ball, at rest, is hit by a 1.0 kg metal ball moving at 4.0 m/s. The 3.0 kg ball moves forward at
the 1.0 kg ball bounces back at 2.0 m/s.
(a) What is the total kinetic energy before the collision?
(b) What is the total kinetic energy after the collision?
(c) How much energy is transferred from the small ball to the large ball?
2.0 m/s and
26. When a 50.0 kg person hangs from a 20.0 m bungee cord it stretches to a length of 32.0 m.
(a) Find the spring constant of the bungee cord, assuming it obeys Hooke's law.
(b) How much work is required to stretch the cord by this much?
27. A spring with a force constant of 5.20 N/m has a relaxed length of 2.45 m. When a mass is attached to the end of the spring and
allowed to come to rest, the vertical length of the spring is 3.57 m. Calculate the elastic potential energy stored in the spring.
28. The staples inside a stapler are kept in place by a spring with a relaxed length of 0.115 m. If the spring constant is 51.0 N/m, how
much elastic potential energy is store in the spring when its length is 0.150 m?
29. A 6.0 kg metal ball moving at 4.0 m/s hits a 6.0 kg ball of putty at rest and sticks to it. The two go on at 2.0 m/s.
(a) What is the kinetic energy of the metal ball before it hits?
(b) What is the kinetic energy of the metal ball after it hits?
(c) What is the kinetic energy of the putty ball after being hit?
(d) How much energy does the metal ball lose in the collision?
(e) How much kinetic energy does the putty ball gain in the collision?
(f) What happened to the rest of the energy?